#include "../camera_models/CataCamera.h"

#include <cmath>
#include <cstdio>
#include <Eigen/Dense>
#include <iomanip>
#include <iostream>
#include <opencv2/calib3d/calib3d.hpp>
#include <opencv2/core/eigen.hpp>
#include <opencv2/imgproc/imgproc.hpp>

#include "../gpl/gpl.h"

namespace camodocal {

CataCamera::Parameters::Parameters():
  Camera::Parameters(MEI),
  m_xi(0.0),
  m_k1(0.0),
  m_k2(0.0),
  m_p1(0.0),
  m_p2(0.0),
  m_gamma1(0.0),
  m_gamma2(0.0),
  m_u0(0.0),
  m_v0(0.0) {
}

CataCamera::Parameters::Parameters(const std::string& cameraName,
                                   int                w,
                                   int                h,
                                   double             xi,
                                   double             k1,
                                   double             k2,
                                   double             p1,
                                   double             p2,
                                   double             gamma1,
                                   double             gamma2,
                                   double             u0,
                                   double             v0):
  Camera::Parameters(MEI, cameraName, w, h),
  m_xi(xi),
  m_k1(k1),
  m_k2(k2),
  m_p1(p1),
  m_p2(p2),
  m_gamma1(gamma1),
  m_gamma2(gamma2),
  m_u0(u0),
  m_v0(v0) {
}

double&
CataCamera::Parameters::xi(void) {
  return m_xi;
}

double&
CataCamera::Parameters::k1(void) {
  return m_k1;
}

double&
CataCamera::Parameters::k2(void) {
  return m_k2;
}

double&
CataCamera::Parameters::p1(void) {
  return m_p1;
}

double&
CataCamera::Parameters::p2(void) {
  return m_p2;
}

double&
CataCamera::Parameters::gamma1(void) {
  return m_gamma1;
}

double&
CataCamera::Parameters::gamma2(void) {
  return m_gamma2;
}

double&
CataCamera::Parameters::u0(void) {
  return m_u0;
}

double&
CataCamera::Parameters::v0(void) {
  return m_v0;
}

double
CataCamera::Parameters::xi(void) const {
  return m_xi;
}

double
CataCamera::Parameters::k1(void) const {
  return m_k1;
}

double
CataCamera::Parameters::k2(void) const {
  return m_k2;
}

double
CataCamera::Parameters::p1(void) const {
  return m_p1;
}

double
CataCamera::Parameters::p2(void) const {
  return m_p2;
}

double
CataCamera::Parameters::gamma1(void) const {
  return m_gamma1;
}

double
CataCamera::Parameters::gamma2(void) const {
  return m_gamma2;
}

double
CataCamera::Parameters::u0(void) const {
  return m_u0;
}

double
CataCamera::Parameters::v0(void) const {
  return m_v0;
}

bool CataCamera::Parameters::readFromYamlFile(const std::string& filename) {
  cv::FileStorage fs(filename, cv::FileStorage::READ);

  if(!fs.isOpened()) {
    return false;
  }

  if(!fs["model_type"].isNone()) {
    std::string sModelType;
    fs["model_type"] >> sModelType;

    if(sModelType.compare("MEI") != 0) {
      return false;
    }
  }

  m_modelType = MEI;
  fs["camera_name"] >> m_cameraName;
  m_imageWidth  = static_cast<int>(fs["image_width"]);
  m_imageHeight = static_cast<int>(fs["image_height"]);

  cv::FileNode n = fs["mirror_parameters"];
  m_xi           = static_cast<double>(n["xi"]);

  n    = fs["distortion_parameters"];
  m_k1 = static_cast<double>(n["k1"]);
  m_k2 = static_cast<double>(n["k2"]);
  m_p1 = static_cast<double>(n["p1"]);
  m_p2 = static_cast<double>(n["p2"]);

  n        = fs["projection_parameters"];
  m_gamma1 = static_cast<double>(n["gamma1"]);
  m_gamma2 = static_cast<double>(n["gamma2"]);
  m_u0     = static_cast<double>(n["u0"]);
  m_v0     = static_cast<double>(n["v0"]);

  return true;
}

void CataCamera::Parameters::writeToYamlFile(const std::string& filename) const {
  cv::FileStorage fs(filename, cv::FileStorage::WRITE);

  fs << "model_type"
     << "MEI";
  fs << "camera_name" << m_cameraName;
  fs << "image_width" << m_imageWidth;
  fs << "image_height" << m_imageHeight;

  // mirror: xi
  fs << "mirror_parameters";
  fs << "{"
     << "xi" << m_xi << "}";

  // radial distortion: k1, k2
  // tangential distortion: p1, p2
  fs << "distortion_parameters";
  fs << "{"
     << "k1" << m_k1
     << "k2" << m_k2
     << "p1" << m_p1
     << "p2" << m_p2 << "}";

  // projection: gamma1, gamma2, u0, v0
  fs << "projection_parameters";
  fs << "{"
     << "gamma1" << m_gamma1
     << "gamma2" << m_gamma2
     << "u0" << m_u0
     << "v0" << m_v0 << "}";

  fs.release();
}

CataCamera::Parameters&
CataCamera::Parameters::operator=(const CataCamera::Parameters& other) {
  if(this != &other) {
    m_modelType   = other.m_modelType;
    m_cameraName  = other.m_cameraName;
    m_imageWidth  = other.m_imageWidth;
    m_imageHeight = other.m_imageHeight;
    m_xi          = other.m_xi;
    m_k1          = other.m_k1;
    m_k2          = other.m_k2;
    m_p1          = other.m_p1;
    m_p2          = other.m_p2;
    m_gamma1      = other.m_gamma1;
    m_gamma2      = other.m_gamma2;
    m_u0          = other.m_u0;
    m_v0          = other.m_v0;
  }

  return *this;
}

std::ostream&
operator<<(std::ostream& out, const CataCamera::Parameters& params) {
  out << "Camera Parameters:" << std::endl;
  out << "    model_type "
      << "MEI" << std::endl;
  out << "   camera_name " << params.m_cameraName << std::endl;
  out << "   image_width " << params.m_imageWidth << std::endl;
  out << "  image_height " << params.m_imageHeight << std::endl;

  out << "Mirror Parameters" << std::endl;
  out << std::fixed << std::setprecision(10);
  out << "            xi " << params.m_xi << std::endl;

  // radial distortion: k1, k2
  // tangential distortion: p1, p2
  out << "Distortion Parameters" << std::endl;
  out << "            k1 " << params.m_k1 << std::endl
      << "            k2 " << params.m_k2 << std::endl
      << "            p1 " << params.m_p1 << std::endl
      << "            p2 " << params.m_p2 << std::endl;

  // projection: gamma1, gamma2, u0, v0
  out << "Projection Parameters" << std::endl;
  out << "        gamma1 " << params.m_gamma1 << std::endl
      << "        gamma2 " << params.m_gamma2 << std::endl
      << "            u0 " << params.m_u0 << std::endl
      << "            v0 " << params.m_v0 << std::endl;

  return out;
}

CataCamera::CataCamera():
  m_inv_K11(1.0),
  m_inv_K13(0.0),
  m_inv_K22(1.0),
  m_inv_K23(0.0),
  m_noDistortion(true) {
}

CataCamera::CataCamera(const std::string& cameraName,
                       int                imageWidth,
                       int                imageHeight,
                       double             xi,
                       double             k1,
                       double             k2,
                       double             p1,
                       double             p2,
                       double             gamma1,
                       double             gamma2,
                       double             u0,
                       double             v0):
  mParameters(cameraName, imageWidth, imageHeight, xi, k1, k2, p1, p2, gamma1, gamma2, u0, v0) {
  if((mParameters.k1() == 0.0) &&
     (mParameters.k2() == 0.0) &&
     (mParameters.p1() == 0.0) &&
     (mParameters.p2() == 0.0)) {
    m_noDistortion = true;
  }
  else {
    m_noDistortion = false;
  }

  // Inverse camera projection matrix parameters
  m_inv_K11 = 1.0 / mParameters.gamma1();
  m_inv_K13 = -mParameters.u0() / mParameters.gamma1();
  m_inv_K22 = 1.0 / mParameters.gamma2();
  m_inv_K23 = -mParameters.v0() / mParameters.gamma2();
}

CataCamera::CataCamera(const CataCamera::Parameters& params):
  mParameters(params) {
  if((mParameters.k1() == 0.0) &&
     (mParameters.k2() == 0.0) &&
     (mParameters.p1() == 0.0) &&
     (mParameters.p2() == 0.0)) {
    m_noDistortion = true;
  }
  else {
    m_noDistortion = false;
  }

  // Inverse camera projection matrix parameters
  m_inv_K11 = 1.0 / mParameters.gamma1();
  m_inv_K13 = -mParameters.u0() / mParameters.gamma1();
  m_inv_K22 = 1.0 / mParameters.gamma2();
  m_inv_K23 = -mParameters.v0() / mParameters.gamma2();
}

Camera::ModelType
CataCamera::modelType(void) const {
  return mParameters.modelType();
}

const std::string&
CataCamera::cameraName(void) const {
  return mParameters.cameraName();
}

int CataCamera::imageWidth(void) const {
  return mParameters.imageWidth();
}

int CataCamera::imageHeight(void) const {
  return mParameters.imageHeight();
}

void CataCamera::estimateIntrinsics(const cv::Size&                              boardSize,
                                    const std::vector<std::vector<cv::Point3f>>& objectPoints,
                                    const std::vector<std::vector<cv::Point2f>>& imagePoints) {
  Parameters params = getParameters();

  double u0 = params.imageWidth() / 2.0;
  double v0 = params.imageHeight() / 2.0;

  double gamma0       = 0.0;
  double minReprojErr = std::numeric_limits<double>::max();

  std::vector<cv::Mat> rvecs, tvecs;
  rvecs.assign(objectPoints.size(), cv::Mat());
  tvecs.assign(objectPoints.size(), cv::Mat());

  params.xi() = 1.0;
  params.k1() = 0.0;
  params.k2() = 0.0;
  params.p1() = 0.0;
  params.p2() = 0.0;
  params.u0() = u0;
  params.v0() = v0;

  // Initialize gamma (focal length)
  // Use non-radial line image and xi = 1
  for(size_t i = 0; i < imagePoints.size(); ++i) {
    for(int r = 0; r < boardSize.height; ++r) {
      cv::Mat P(boardSize.width, 4, CV_64F);
      for(int c = 0; c < boardSize.width; ++c) {
        const cv::Point2f& imagePoint = imagePoints.at(i).at(r * boardSize.width + c);

        double u = imagePoint.x - u0;
        double v = imagePoint.y - v0;

        P.at<double>(c, 0) = u;
        P.at<double>(c, 1) = v;
        P.at<double>(c, 2) = 0.5;
        P.at<double>(c, 3) = -0.5 * (square(u) + square(v));
      }

      cv::Mat C;
      cv::SVD::solveZ(P, C);

      double t = square(C.at<double>(0)) + square(C.at<double>(1)) + C.at<double>(2) * C.at<double>(3);
      if(t < 0.0) {
        continue;
      }

      // check that line image is not radial
      double d  = sqrt(1.0 / t);
      double nx = C.at<double>(0) * d;
      double ny = C.at<double>(1) * d;
      if(hypot(nx, ny) > 0.95) {
        continue;
      }

      double gamma = sqrt(C.at<double>(2) / C.at<double>(3));

      params.gamma1() = gamma;
      params.gamma2() = gamma;
      setParameters(params);

      for(size_t j = 0; j < objectPoints.size(); ++j) {
        estimateExtrinsics(objectPoints.at(j), imagePoints.at(j), rvecs.at(j), tvecs.at(j));
      }

      double reprojErr = reprojectionError(objectPoints, imagePoints, rvecs, tvecs, cv::noArray());

      if(reprojErr < minReprojErr) {
        minReprojErr = reprojErr;
        gamma0       = gamma;
      }
    }
  }

  if(gamma0 <= 0.0 && minReprojErr >= std::numeric_limits<double>::max()) {
    std::cout << "[" << params.cameraName() << "] "
              << "# INFO: CataCamera model fails with given data. " << std::endl;

    return;
  }

  params.gamma1() = gamma0;
  params.gamma2() = gamma0;
  setParameters(params);
}

/** 
 * \brief Lifts a point from the image plane to the unit sphere
 *
 * \param p image coordinates
 * \param P coordinates of the point on the sphere
 */
void CataCamera::liftSphere(const Eigen::Vector2d& p, Eigen::Vector3d& P) const {
  double mx_d, my_d, mx2_d, mxy_d, my2_d, mx_u, my_u;
  double rho2_d, rho4_d, radDist_d, Dx_d, Dy_d, inv_denom_d;
  double lambda;

  // Lift points to normalised plane
  mx_d = m_inv_K11 * p(0) + m_inv_K13;
  my_d = m_inv_K22 * p(1) + m_inv_K23;

  if(m_noDistortion) {
    mx_u = mx_d;
    my_u = my_d;
  }
  else {
    // Apply inverse distortion model
    if(0) {
      double k1 = mParameters.k1();
      double k2 = mParameters.k2();
      double p1 = mParameters.p1();
      double p2 = mParameters.p2();

      // Inverse distortion model
      // proposed by Heikkila
      mx2_d       = mx_d * mx_d;
      my2_d       = my_d * my_d;
      mxy_d       = mx_d * my_d;
      rho2_d      = mx2_d + my2_d;
      rho4_d      = rho2_d * rho2_d;
      radDist_d   = k1 * rho2_d + k2 * rho4_d;
      Dx_d        = mx_d * radDist_d + p2 * (rho2_d + 2 * mx2_d) + 2 * p1 * mxy_d;
      Dy_d        = my_d * radDist_d + p1 * (rho2_d + 2 * my2_d) + 2 * p2 * mxy_d;
      inv_denom_d = 1 / (1 + 4 * k1 * rho2_d + 6 * k2 * rho4_d + 8 * p1 * my_d + 8 * p2 * mx_d);

      mx_u = mx_d - inv_denom_d * Dx_d;
      my_u = my_d - inv_denom_d * Dy_d;
    }
    else {
      // Recursive distortion model
      int             n = 6;
      Eigen::Vector2d d_u;
      distortion(Eigen::Vector2d(mx_d, my_d), d_u);
      // Approximate value
      mx_u = mx_d - d_u(0);
      my_u = my_d - d_u(1);

      for(int i = 1; i < n; ++i) {
        distortion(Eigen::Vector2d(mx_u, my_u), d_u);
        mx_u = mx_d - d_u(0);
        my_u = my_d - d_u(1);
      }
    }
  }

  // Lift normalised points to the sphere (inv_hslash)
  double xi = mParameters.xi();
  if(xi == 1.0) {
    lambda = 2.0 / (mx_u * mx_u + my_u * my_u + 1.0);
    P << lambda * mx_u, lambda * my_u, lambda - 1.0;
  }
  else {
    lambda = (xi + sqrt(1.0 + (1.0 - xi * xi) * (mx_u * mx_u + my_u * my_u))) / (1.0 + mx_u * mx_u + my_u * my_u);
    P << lambda * mx_u, lambda * my_u, lambda - xi;
  }
}

/** 
 * \brief Lifts a point from the image plane to its projective ray
 *
 * \param p image coordinates
 * \param P coordinates of the projective ray
 */
void CataCamera::liftProjective(const Eigen::Vector2d& p, Eigen::Vector3d& P) const {
  double mx_d, my_d, mx2_d, mxy_d, my2_d, mx_u, my_u;
  double rho2_d, rho4_d, radDist_d, Dx_d, Dy_d, inv_denom_d;
  //double lambda;

  // Lift points to normalised plane
  mx_d = m_inv_K11 * p(0) + m_inv_K13;
  my_d = m_inv_K22 * p(1) + m_inv_K23;

  if(m_noDistortion) {
    mx_u = mx_d;
    my_u = my_d;
  }
  else {
    if(0) {
      double k1 = mParameters.k1();
      double k2 = mParameters.k2();
      double p1 = mParameters.p1();
      double p2 = mParameters.p2();

      // Apply inverse distortion model
      // proposed by Heikkila
      mx2_d       = mx_d * mx_d;
      my2_d       = my_d * my_d;
      mxy_d       = mx_d * my_d;
      rho2_d      = mx2_d + my2_d;
      rho4_d      = rho2_d * rho2_d;
      radDist_d   = k1 * rho2_d + k2 * rho4_d;
      Dx_d        = mx_d * radDist_d + p2 * (rho2_d + 2 * mx2_d) + 2 * p1 * mxy_d;
      Dy_d        = my_d * radDist_d + p1 * (rho2_d + 2 * my2_d) + 2 * p2 * mxy_d;
      inv_denom_d = 1 / (1 + 4 * k1 * rho2_d + 6 * k2 * rho4_d + 8 * p1 * my_d + 8 * p2 * mx_d);

      mx_u = mx_d - inv_denom_d * Dx_d;
      my_u = my_d - inv_denom_d * Dy_d;
    }
    else {
      // Recursive distortion model
      int             n = 8;
      Eigen::Vector2d d_u;
      distortion(Eigen::Vector2d(mx_d, my_d), d_u);
      // Approximate value
      mx_u = mx_d - d_u(0);
      my_u = my_d - d_u(1);

      for(int i = 1; i < n; ++i) {
        distortion(Eigen::Vector2d(mx_u, my_u), d_u);
        mx_u = mx_d - d_u(0);
        my_u = my_d - d_u(1);
      }
    }
  }

  // Obtain a projective ray
  double xi = mParameters.xi();
  if(xi == 1.0) {
    P << mx_u, my_u, (1.0 - mx_u * mx_u - my_u * my_u) / 2.0;
  }
  else {
    // Reuse variable
    rho2_d = mx_u * mx_u + my_u * my_u;
    P << mx_u, my_u, 1.0 - xi * (rho2_d + 1.0) / (xi + sqrt(1.0 + (1.0 - xi * xi) * rho2_d));
  }
}

/**
 * \brief Project a 3D point (\a x,\a y,\a z) to the image plane in (\a u,\a v)
 *
 * \param P 3D point coordinates
 * \param p return value, contains the image point coordinates
 */
void CataCamera::spaceToPlane(const Eigen::Vector3d& P, Eigen::Vector2d& p) const {
  Eigen::Vector2d p_u, p_d;

  // Project points to the normalised plane
  double z = P(2) + mParameters.xi() * P.norm();
  p_u << P(0) / z, P(1) / z;

  if(m_noDistortion) {
    p_d = p_u;
  }
  else {
    // Apply distortion
    Eigen::Vector2d d_u;
    distortion(p_u, d_u);
    p_d = p_u + d_u;
  }

  // Apply generalised projection matrix
  p << mParameters.gamma1() * p_d(0) + mParameters.u0(),
    mParameters.gamma2() * p_d(1) + mParameters.v0();
}

#if 0
/** 
 * \brief Project a 3D point to the image plane and calculate Jacobian
 *
 * \param P 3D point coordinates
 * \param p return value, contains the image point coordinates
 */
void
CataCamera::spaceToPlane(const Eigen::Vector3d& P, Eigen::Vector2d& p,
                        Eigen::Matrix<double,2,3>& J) const
{
    double xi = mParameters.xi();

    Eigen::Vector2d p_u, p_d;
    double norm, inv_denom;
    double dxdmx, dydmx, dxdmy, dydmy;

    norm = P.norm();
    // Project points to the normalised plane
    inv_denom = 1.0 / (P(2) + xi * norm);
    p_u << inv_denom * P(0), inv_denom * P(1);

    // Calculate jacobian
    inv_denom = inv_denom * inv_denom / norm;
    double dudx = inv_denom * (norm * P(2) + xi * (P(1) * P(1) + P(2) * P(2)));
    double dvdx = -inv_denom * xi * P(0) * P(1);
    double dudy = dvdx;
    double dvdy = inv_denom * (norm * P(2) + xi * (P(0) * P(0) + P(2) * P(2)));
    inv_denom = inv_denom * (-xi * P(2) - norm); // reuse variable
    double dudz = P(0) * inv_denom;
    double dvdz = P(1) * inv_denom;

    if (m_noDistortion)
    {
        p_d = p_u;
    }
    else
    {
        // Apply distortion
        Eigen::Vector2d d_u;
        distortion(p_u, d_u);
        p_d = p_u + d_u;
    }

    double gamma1 = mParameters.gamma1();
    double gamma2 = mParameters.gamma2();

    // Make the product of the jacobians
    // and add projection matrix jacobian
    inv_denom = gamma1 * (dudx * dxdmx + dvdx * dxdmy); // reuse
    dvdx = gamma2 * (dudx * dydmx + dvdx * dydmy);
    dudx = inv_denom;

    inv_denom = gamma1 * (dudy * dxdmx + dvdy * dxdmy); // reuse
    dvdy = gamma2 * (dudy * dydmx + dvdy * dydmy);
    dudy = inv_denom;

    inv_denom = gamma1 * (dudz * dxdmx + dvdz * dxdmy); // reuse
    dvdz = gamma2 * (dudz * dydmx + dvdz * dydmy);
    dudz = inv_denom;
    
    // Apply generalised projection matrix
    p << gamma1 * p_d(0) + mParameters.u0(),
         gamma2 * p_d(1) + mParameters.v0();

    J << dudx, dudy, dudz,
         dvdx, dvdy, dvdz;
}
#endif

/** 
 * \brief Projects an undistorted 2D point p_u to the image plane
 *
 * \param p_u 2D point coordinates
 * \return image point coordinates
 */
void CataCamera::undistToPlane(const Eigen::Vector2d& p_u, Eigen::Vector2d& p) const {
  Eigen::Vector2d p_d;

  if(m_noDistortion) {
    p_d = p_u;
  }
  else {
    // Apply distortion
    Eigen::Vector2d d_u;
    distortion(p_u, d_u);
    p_d = p_u + d_u;
  }

  // Apply generalised projection matrix
  p << mParameters.gamma1() * p_d(0) + mParameters.u0(),
    mParameters.gamma2() * p_d(1) + mParameters.v0();
}

/** 
 * \brief Apply distortion to input point (from the normalised plane)
 *  
 * \param p_u undistorted coordinates of point on the normalised plane
 * \return to obtain the distorted point: p_d = p_u + d_u
 */
void CataCamera::distortion(const Eigen::Vector2d& p_u, Eigen::Vector2d& d_u) const {
  double k1 = mParameters.k1();
  double k2 = mParameters.k2();
  double p1 = mParameters.p1();
  double p2 = mParameters.p2();

  double mx2_u, my2_u, mxy_u, rho2_u, rad_dist_u;

  mx2_u      = p_u(0) * p_u(0);
  my2_u      = p_u(1) * p_u(1);
  mxy_u      = p_u(0) * p_u(1);
  rho2_u     = mx2_u + my2_u;
  rad_dist_u = k1 * rho2_u + k2 * rho2_u * rho2_u;
  d_u << p_u(0) * rad_dist_u + 2.0 * p1 * mxy_u + p2 * (rho2_u + 2.0 * mx2_u),
    p_u(1) * rad_dist_u + 2.0 * p2 * mxy_u + p1 * (rho2_u + 2.0 * my2_u);
}

/** 
 * \brief Apply distortion to input point (from the normalised plane)
 *        and calculate Jacobian
 *
 * \param p_u undistorted coordinates of point on the normalised plane
 * \return to obtain the distorted point: p_d = p_u + d_u
 */
void CataCamera::distortion(const Eigen::Vector2d& p_u, Eigen::Vector2d& d_u, Eigen::Matrix2d& J) const {
  double k1 = mParameters.k1();
  double k2 = mParameters.k2();
  double p1 = mParameters.p1();
  double p2 = mParameters.p2();

  double mx2_u, my2_u, mxy_u, rho2_u, rad_dist_u;

  mx2_u      = p_u(0) * p_u(0);
  my2_u      = p_u(1) * p_u(1);
  mxy_u      = p_u(0) * p_u(1);
  rho2_u     = mx2_u + my2_u;
  rad_dist_u = k1 * rho2_u + k2 * rho2_u * rho2_u;
  d_u << p_u(0) * rad_dist_u + 2.0 * p1 * mxy_u + p2 * (rho2_u + 2.0 * mx2_u),
    p_u(1) * rad_dist_u + 2.0 * p2 * mxy_u + p1 * (rho2_u + 2.0 * my2_u);

  double dxdmx = 1.0 + rad_dist_u + k1 * 2.0 * mx2_u + k2 * rho2_u * 4.0 * mx2_u + 2.0 * p1 * p_u(1) + 6.0 * p2 * p_u(0);
  double dydmx = k1 * 2.0 * p_u(0) * p_u(1) + k2 * 4.0 * rho2_u * p_u(0) * p_u(1) + p1 * 2.0 * p_u(0) + 2.0 * p2 * p_u(1);
  double dxdmy = dydmx;
  double dydmy = 1.0 + rad_dist_u + k1 * 2.0 * my2_u + k2 * rho2_u * 4.0 * my2_u + 6.0 * p1 * p_u(1) + 2.0 * p2 * p_u(0);

  J << dxdmx, dxdmy,
    dydmx, dydmy;
}

void CataCamera::initUndistortMap(cv::Mat& map1, cv::Mat& map2, double fScale) const {
  cv::Size imageSize(mParameters.imageWidth(), mParameters.imageHeight());

  cv::Mat mapX = cv::Mat::zeros(imageSize, CV_32F);
  cv::Mat mapY = cv::Mat::zeros(imageSize, CV_32F);

  for(int v = 0; v < imageSize.height; ++v) {
    for(int u = 0; u < imageSize.width; ++u) {
      double mx_u = m_inv_K11 / fScale * u + m_inv_K13 / fScale;
      double my_u = m_inv_K22 / fScale * v + m_inv_K23 / fScale;

      double xi = mParameters.xi();
      double d2 = mx_u * mx_u + my_u * my_u;

      Eigen::Vector3d P;
      P << mx_u, my_u, 1.0 - xi * (d2 + 1.0) / (xi + sqrt(1.0 + (1.0 - xi * xi) * d2));

      Eigen::Vector2d p;
      spaceToPlane(P, p);

      mapX.at<float>(v, u) = p(0);
      mapY.at<float>(v, u) = p(1);
    }
  }

  cv::convertMaps(mapX, mapY, map1, map2, CV_32FC1, false);
}

cv::Mat
CataCamera::initUndistortRectifyMap(cv::Mat& map1, cv::Mat& map2, float fx, float fy, cv::Size imageSize, float cx, float cy, cv::Mat rmat) const {
  if(imageSize == cv::Size(0, 0)) {
    imageSize = cv::Size(mParameters.imageWidth(), mParameters.imageHeight());
  }

  cv::Mat mapX = cv::Mat::zeros(imageSize.height, imageSize.width, CV_32F);
  cv::Mat mapY = cv::Mat::zeros(imageSize.height, imageSize.width, CV_32F);

  Eigen::Matrix3f K_rect;

  if(cx == -1.0f && cy == -1.0f) {
    K_rect << fx, 0, imageSize.width / 2,
      0, fy, imageSize.height / 2,
      0, 0, 1;
  }
  else {
    K_rect << fx, 0, cx,
      0, fy, cy,
      0, 0, 1;
  }

  if(fx == -1.0f || fy == -1.0f) {
    K_rect(0, 0) = mParameters.gamma1();
    K_rect(1, 1) = mParameters.gamma2();
  }

  Eigen::Matrix3f K_rect_inv = K_rect.inverse();

  Eigen::Matrix3f R, R_inv;
  cv::cv2eigen(rmat, R);
  R_inv = R.inverse();

  for(int v = 0; v < imageSize.height; ++v) {
    for(int u = 0; u < imageSize.width; ++u) {
      Eigen::Vector3f xo;
      xo << u, v, 1;

      Eigen::Vector3f uo = R_inv * K_rect_inv * xo;

      Eigen::Vector2d p;
      spaceToPlane(uo.cast<double>(), p);

      mapX.at<float>(v, u) = p(0);
      mapY.at<float>(v, u) = p(1);
    }
  }

  cv::convertMaps(mapX, mapY, map1, map2, CV_32FC1, false);

  cv::Mat K_rect_cv;
  cv::eigen2cv(K_rect, K_rect_cv);
  return K_rect_cv;
}

int CataCamera::parameterCount(void) const {
  return 9;
}

const CataCamera::Parameters&
CataCamera::getParameters(void) const {
  return mParameters;
}

void CataCamera::setParameters(const CataCamera::Parameters& parameters) {
  mParameters = parameters;

  if((mParameters.k1() == 0.0) &&
     (mParameters.k2() == 0.0) &&
     (mParameters.p1() == 0.0) &&
     (mParameters.p2() == 0.0)) {
    m_noDistortion = true;
  }
  else {
    m_noDistortion = false;
  }

  m_inv_K11 = 1.0 / mParameters.gamma1();
  m_inv_K13 = -mParameters.u0() / mParameters.gamma1();
  m_inv_K22 = 1.0 / mParameters.gamma2();
  m_inv_K23 = -mParameters.v0() / mParameters.gamma2();
}

void CataCamera::readParameters(const std::vector<double>& parameterVec) {
  if((int)parameterVec.size() != parameterCount()) {
    return;
  }

  Parameters params = getParameters();

  params.xi()     = parameterVec.at(0);
  params.k1()     = parameterVec.at(1);
  params.k2()     = parameterVec.at(2);
  params.p1()     = parameterVec.at(3);
  params.p2()     = parameterVec.at(4);
  params.gamma1() = parameterVec.at(5);
  params.gamma2() = parameterVec.at(6);
  params.u0()     = parameterVec.at(7);
  params.v0()     = parameterVec.at(8);

  setParameters(params);
}

void CataCamera::writeParameters(std::vector<double>& parameterVec) const {
  parameterVec.resize(parameterCount());
  parameterVec.at(0) = mParameters.xi();
  parameterVec.at(1) = mParameters.k1();
  parameterVec.at(2) = mParameters.k2();
  parameterVec.at(3) = mParameters.p1();
  parameterVec.at(4) = mParameters.p2();
  parameterVec.at(5) = mParameters.gamma1();
  parameterVec.at(6) = mParameters.gamma2();
  parameterVec.at(7) = mParameters.u0();
  parameterVec.at(8) = mParameters.v0();
}

void CataCamera::writeParametersToYamlFile(const std::string& filename) const {
  mParameters.writeToYamlFile(filename);
}

std::string
CataCamera::parametersToString(void) const {
  std::ostringstream oss;
  oss << mParameters;

  return oss.str();
}

} // namespace camodocal
